One of the most extensively studied topics in Differential Geometry is minimal surfaces. This subject has connections with a wide range of mathematics areas, such as complex analysis, partial differential equations and topology. A classic problem in this context is the Plateau problem and recently much attention has been given to problems with the free boundary condition. In this talk, we will present some results about classification for constant mean curvature (CMC) surfaces with the free boundary condition in certain spaces. This is a joint work with Ezequiel Barbosa (UFMG) and Edno Pereira (UFSJ).